Experiment: Spin the spinner below then select one ball from the box designated by the spinner.
A) In the experiment, selecting R pays $2 and selecting W pays $4. It costs $3 to play. What is the expected value?
B) What does your answer in part A mean?

Question

Experiment: Spin the spinner below then select one ball from the box designated by the spinner.  
A) In the experiment, selecting R pays $2 and selecting W pays $4. It costs $3 to play. What is the expected value? 
B) What does your answer in part A mean?

Quizplus · Accepted Answer

The Answer is A) P(R) =

\frac { 1 } { 3 } \cdot \frac { 1 } { 4 } + \frac { 2 } { 3 } \cdot \frac { 3 } { 5 } = \frac { 1 } { 12 } + \frac { 2 } { 5 } = \frac { 29 } { 60 }

and P(W) =

\frac { 1 } { 3 } \cdot \frac { 3 } { 4 } + \frac { 2 } { 3 } \cdot \frac { 2 } { 5 } = \frac { 1 } { 4 } + \frac { 4 } { 15 } = \frac { 31 } { 50 }

.

So,

\frac { 22 } { 60 } \cdot 2 + \frac { 31 } { 60 } \cdot 4 - 3 = \frac { 1 } { 30 } \approx 0.033

dollar.

B) If you do the experiment many, many times, you will win an average of about $0.033 per game.

Experiment: Spin the Spinner Below Then Select One Ball from the Box